Final answer:
The probability that a continuous uniform random variable X~U(4.5,18.5) is less than 11 is approximately 0.4643 or 46.43%.
Step-by-step explanation:
The student is dealing with a continuous uniform random variable, specifically finding the probability that the variable is less than a certain value. For a uniform distribution X~U(a, b), the probability density function is f(x) = 1/(b-a) for a≤x≤b, and the probability that X is less than a certain value k within the range is P(X
By performing the calculations, we get:
P(x<11) = (11-4.5)/(18.5-4.5) = 6.5/14 = 0.4643.
Therefore, the probability that x is less than 11 for our uniform distribution is approximately 0.4643 or 46.43%.